3u(u+4)(u+3)=0

Solution for 3u(u+4)(u+3)=0 equation:

Simplifying
3u(u + 4)(u + 3) = 0

Reorder the terms:
3u(4 + u)(u + 3) = 0

Reorder the terms:
3u(4 + u)(3 + u) = 0

Multiply (4 + u) * (3 + u)
3u(4(3 + u) + u(3 + u)) = 0
3u((3 * 4 + u * 4) + u(3 + u)) = 0
3u((12 + 4u) + u(3 + u)) = 0
3u(12 + 4u + (3 * u + u * u)) = 0
3u(12 + 4u + (3u + u2)) = 0

Combine like terms: 4u + 3u = 7u
3u(12 + 7u + u2) = 0
(12 * 3u + 7u * 3u + u2 * 3u) = 0
(36u + 21u2 + 3u3) = 0

Solving
36u + 21u2 + 3u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3u'.
3u(12 + 7u + u2) = 0

Factor a trinomial.
3u((4 + u)(3 + u)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'u' equal to zero and attempt to solve:

Simplifying
u = 0

Solving
u = 0

Move all terms containing u to the left, all other terms to the right.

Simplifying
u = 0
Subproblem 2
Set the factor '(4 + u)' equal to zero and attempt to solve:

Simplifying
4 + u = 0

Solving
4 + u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + u = 0 + -4
u = 0 + -4

Combine like terms: 0 + -4 = -4
u = -4

Simplifying
u = -4
Subproblem 3
Set the factor '(3 + u)' equal to zero and attempt to solve:

Simplifying
3 + u = 0

Solving
3 + u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + u = 0 + -3
u = 0 + -3

Combine like terms: 0 + -3 = -3
u = -3

Simplifying
u = -3
Solution
u = {0, -4, -3}